I hear ya fellas. Limestone and most sedimentary rocks are the ones to really watch. If all rocks exploded easily and in a violent way, there would be a whole lot of dead people from camp fires. Usually they just make a little pop and break in half. If you go to a landscaping supply yard and ask for river rocks, they will take you to a pile of round rocks. Not rocks in water. Sorry, I thought that was a fairly common term.
The reason I made the suggestion of the rocks was because the shelter is not a tipi, but shaped like a sweat lodge. Unless you keep all the wood inside the tipi with you, you will need to leave the shelter. Sweat lodges get quite warm and stay that way pretty well. If you want a tipi type shelter and firepit, than the shelter needs to be rebuilt.
You could also build a radiant heat wall. Then the fire could be outside and still heat the shelter. How much heat do you need in there. In the winter a candle lantern heats my tent plenty. If the top doesn't have a heat releasing hole in it, it will stay pretty good in there with just your body heat.. There are options other than a fire in the shelter, but you can't turn a wigam into a tipi, they are different shapes for a reason.